If we had a magnet we move it towards a solenoid a half sine wave current is induced when we make it move back, the other half is induced, inducing an AC current in the solenoid.
What if the magnet moves towards the solenoid, inside it and comes the other side? Will a current be induced while the magnet is moving inside (not entering nor exiting the solenoid, given that length of solenoid is much bigger than that of the magnet).
If yes, what kind of current will be induced? If no, why? If AC current is induced, how would one calculate its frequency?